Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia, 30303, USA.
J Math Neurosci. 2011 Jul 11;1(1):6. doi: 10.1186/2190-8567-1-6.
Development of effective and plausible numerical tools is an imperative task for thorough studies of nonlinear dynamics in life science applications.
We have developed a complementary suite of computational tools for two-parameter screening of dynamics in neuronal models. We test a 'brute-force' effectiveness of neuroscience plausible techniques specifically tailored for the examination of temporal characteristics, such duty cycle of bursting, interspike interval, spike number deviation in the phenomenological Hindmarsh-Rose model of a bursting neuron and compare the results obtained by calculus-based tools for evaluations of an entire spectrum of Lyapunov exponents broadly employed in studies of nonlinear systems.
We have found that the results obtained either way agree exceptionally well, and can identify and differentiate between various fine structures of complex dynamics and underlying global bifurcations in this exemplary model. Our future planes are to enhance the applicability of this computational suite for understanding of polyrhythmic bursting patterns and their functional transformations in small networks.
开发有效且合理的数值工具对于深入研究生命科学应用中的非线性动力学至关重要。
我们开发了一套用于神经元模型动力学双参数筛选的补充计算工具。我们测试了一种针对时间特征的神经科学合理技术的“强力”有效性，例如爆发神经元的现象学 Hindmarsh-Rose 模型中的爆发的占空比、脉冲间隔、脉冲数偏差，并将通过基于微积分的工具获得的结果进行比较，以评估广泛应用于非线性系统研究的整个 Lyapunov 指数谱。
我们发现无论哪种方法获得的结果都非常吻合，可以识别和区分这个典型模型中复杂动力学的各种精细结构和潜在的全局分岔。我们未来的计划是增强这个计算套件的适用性，以理解小网络中的多韵律爆发模式及其功能转换。
